New approximative kernels improve PDE-G-CNNs for geometric deep learning.
problem Inaccurate approximations of exact kernels in PDE-G-CNNs.
method Developed new approximative kernels that work regardless of spatial anisotropy.
result New kernels provide better error estimates and maintain reflectional symmetries.
Group equivariant and steerable convolutional neural networks (regular and steerable G-CNNs) have recently emerged as a very effective model class for learning from signal data such as 2D and 3D images, video, and other data where symmetries are present. In geometrical terms, regular G-CNNs represent data in terms of s…
B-Spline CNNs on Lie Groups expand G-CNNs to arbitrary groups.
problem Leveraging geometric structure for improved feature learning.
method Lifting feature maps to B-spline expansions on Lie algebra.
result G-CNNs on Lie groups outperform classical 2D CNNs.
PDE-based G-CNNs add geometric symmetries to CNNs without augmentation.
problem Designing CNNs with built-in symmetries like rotation.
method Formulate CNN layers as PDE solvers on homogeneous spaces.
result PDE-G-CNNs achieve better performance with fewer parameters.
We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that enjoys a substantially higher degree of weight sharing than regular convolution la…
Convolutional Neural Networks (CNNs) require a large amount of annotated data to learn from, which is often difficult to obtain in the medical domain. In this paper we show that the sample complexity of CNNs can be significantly improved by using 3D roto-translation group convolutions (G-Convs) instead of the more conv…
Study on geodesic distances on SE(3)/SO(2) in machine learning.
problem Investigating the efficiency of computationally efficient sections in selecting geodesic distances.
method Analyzing geodesic distances on reductive homogeneous spaces, proving the efficiency of minimal distance sections.
result Minimal distance sections are not always geodesic minimizers, but minimal horizontal geodesics are.
Cake wavelets minimize orientation score uncertainty.
problem Minimizing uncertainty in orientation scores.
method Axiomatically derived wavelets for orientation score lifting.
result Uncertainty gap of cake wavelets is less than 1.1.
Generalizes CNNs on homogeneous spaces like Euclidean and spherical surfaces.
problem Classifying and understanding equivariant CNNs on homogeneous spaces.
method Develops a theory for equivariant maps between field spaces of given types.
result Equivariant kernels correspond to the most general kind of equivariant linear maps.
Geometric models improve feature extraction and equivariance in image generation.
problem Improving feature extraction at multiscale levels and reducing network complexity.
method Proposes a geometric generative model based on morphological PDEs and GANs, incorporating equivariance for geometric interpretability.
result Preliminary results show GM-GAN outperforms classical GANs on MNIST data.
The paper generalizes equivariant neural networks on homogeneous spaces to the non-linear setting.
problem Equivariant neural networks on homogeneous spaces.
method Deriving generalized steerability constraints for non-linear equivariant layers.
result The universality of the derived construction for non-linear equivariant layers.
Using predictive models to identify patterns that can act as biomarkers for different neuropathoglogical conditions is becoming highly prevalent. In this paper, we consider the problem of Autism Spectrum Disorder (ASD) classification where previous work has shown that it can be beneficial to incorporate a wide variety …
Paper introduces method to make neural networks symmetrical.
problem Creating symmetrical neural networks for data with inherent symmetries.
method Introduces a method for modifying neural networks to enforce equivariance.
result Group convolutional neural networks are a special case of the introduced framework.
Proposes a graph-based system for personalized news recommendation considering multiple user behaviors.
problem Lack of considering multiple user behaviors in news recommendation systems.
method Builds an interaction behavior graph, applies DeepWalk and G-CNN for news and behavior sequence representations, introduces core and coritivity features.
result Achieves personalized news recommendation considering user's concentration degree of interests.
Combining deep neural networks with structured logic rules is desirable to harness flexibility and reduce uninterpretability of the neural models. We propose a general framework capable of enhancing various types of neural networks (e.g., CNNs and RNNs) with declarative first-order logic rules. Specifically, we develop…
New model generates code from GUI screenshots using attention and hierarchical structure.
problem Challenges in converting abstract image features to code.
method Attention-based hierarchical decoder trained end-to-end.
result Model outperforms state-of-the-art methods on GUI-code datasets.
Advances understanding of neural network generalization via tensor analysis.
problem Understanding the generalizability of deep neural networks.
method Tensor analysis to measure compressibility and generalizability.
result Proposed generalization bound outperforms previous methods, especially for tensor-based networks.
Improved GP model forecasts wireless demand extremes with better uncertainty quantification.
problem Forecasting extreme wireless demand spikes and troughs for network optimization.
method Designed a feature embedding kernel for Gaussian Process models.
result 32% reduction in short-term extreme value prediction error vs. S-ARIMA.
Extends RDS filtering to position-orientation space for better image processing.
problem Enhancing and inpainting images with crossing structures.
method Created a version of RDS filtering using gauge frames, studying generalised diffusion.
result RDS filtering on position-orientation space improves denoising and inpainting of crossing structures.